Twisted torus
Also known as twisted torus, twisted 3D torus, Mobius torus
In plain English
A twisted torus is a torus network whose wraparound links are shifted, like a Mobius strip, so the average number of hops between chips drops further.
Technical definition
A twisted torus is a torus topology in which the wraparound connections along one or more dimensions are offset rather than joining a row directly to itself, which lowers the average and worst-case hop count compared with a plain torus of the same size.
Engineering details
A plain torus connects the two ends of each row, turning a line into a ring and halving the worst-case distance from N to N/2. A twisted torus shifts the wraparound so a row connects to a neighboring row on the far side, spreading traffic across more paths and reducing the average distance again. Google uses this variant in TPU pods, built from 4x4x4 cubes of 64 chips and stitched together by optical circuit switches that preserve the wraparound property across the whole pod.
Why it matters
Hop count sets latency for small collective messages, and the twist buys a few percent of latency without new hardware. The TPU 8i Boardfly topology goes further by abandoning the torus for a high-radix hierarchical fabric, cutting diameter from roughly 16 hops to about 7 at 1,024 to 1,152 chips.
How to read it in InferenceX
The TPU InferenceX preview notes that in many cases the TPU torus has lower latency than a single-hop NVSwitch for small expert-parallel messages, with detailed results deferred to the CollectiveX and NetworkingX lanes.